326_midterm-10 - UBC, ECONOMICS 326 - 003 2010 MIDTERM...

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2010 MIDTERM EXAMINATION There are 3 questions (100 points total). You have 80 minutes. Answer all questions. Question 1. Consider a simple linear regression model: Y i = β 0 + β 1 X i + U i , i = 1 ,...,n ; β 0 6 = 0; E ( U i | X 1 ,...,X n ) = 0 . Define ˆ β 1 = n i =1 ( X i - ¯ X ) Y i n i =1 ( X i - ¯ X ) 2 and ˆ β 0 = ¯ Y - ˆ β 1 ¯ X, ˜ β 1 = n i =1 X i Y i n i =1 X 2 i and ˜ β 0 = 0 , where ¯ X = n - 1 n i =1 X i . Define also ˆ U i = Y i - ˆ β 0 - ˆ β 1 X i , ˜ U i = Y i - ˜ β 1 X i . For each of the following statements, indicate true or false and explain your answers. (a) (6 points) n i =1 ˆ U i = 0. (b) (6 points) n i =1 ˜ U i = 0. (c) (6 points) n i =1 U i = 0. (d) (6 points) E ( U i X 4 i ) = 0. (e) (6 points) In this model, ˆ β 1 is the OLS estimator, and therefore the Gauss- Markov Theorem implies that V ar ± ˆ β 1 | X 1 ,...,X n ² V ar ± ˜ β 1 | X 1 ,...,X n ² . Assume that errors
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This note was uploaded on 03/24/2012 for the course ECON 326 taught by Professor Whisler during the Spring '10 term at The University of British Columbia.

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326_midterm-10 - UBC, ECONOMICS 326 - 003 2010 MIDTERM...

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